I had the exact problem on my 1998 MY 156 (V6) quite recently, and was looking at the dreaded possibility of coughing up GBP 150 for a new speedo. The mechanic at my local Alfa dealership suggested that before I buy a new speedo, he would clean the ABS and gearbox sensors (both of which, apparently, provide inputs to the speedo) and see if that worked. Sure enough ... my speedo is now working without any faults. So cleaning the sensors certainly worked in my case.
Hope that helps.